Cody Arlie ReedResearch + data
All projectsSegregation across the day

Paper · 2026

Segregation across the day

The questionHow does racial segregation change across hours and days, and which theoretical perspectives explain these patterns?

  • Segregation estimation
  • Matrix computation
  • R and C++

ApproachI combined mobile-phone locations with Census demographics and used my matrix formulation to estimate hourly racial segregation in 18 U.S. commuting zones.

Overview

What I found

Racial segregation was highest overnight and lowest during weekday working hours, consistent with compelled mobility. Lower segregation on Friday and Saturday nights offered partial support for cosmopolitanism.

Distributions of hourly racial segregation divided by residential racial segregation for 18 U.S. commuting zones
Hourly versus residential racial segregation · 18 U.S. commuting zones

Each point is one hourly segregation estimate divided by residential segregation in the same commuting zone. A value of 1 means equal segregation; values below 1 mean lower hourly segregation. Boxes contain the middle half of each commuting zone’s hourly ratios.

Open full-size figure

Data and measurement

Estimate segregation as people move.

I developed a method that combines mobile-phone locations with Census demographics to estimate racial segregation hour by hour. The analysis covers 18 large U.S. commuting zones.

  1. 01
    Estimate population composition

    I inferred home tracts from nighttime locations, attached Census demographics, and adjusted for uneven representation in the phone data.

  2. 02
    Construct local environments

    I weighted nearby observations by distance and time to estimate the racial composition around each location.

  3. 03
    Measure change over time

    I calculated 428 hourly segregation estimates per commuting zone using 18 days of observations from January 2020, then compared hourly and residential segregation.

Computation

Formulate the calculation as matrix multiplication.

I developed a high dimensional matrix multiplication approach to estimate local populations across space and time. It combines pairwise proximity weights with demographic frequencies, producing the local compositions needed for the segregation index.

Some matrices contain more than a billion elements. I implemented the calculation in C++ with RcppArmadillo and RcppParallel, using R to coordinate data preparation, estimation, and visualization.

From location records to an hourly segregation estimate
Lₕ = Wₕ FₕL̃ᵢₘₕ = Ω(sᵢ − h) LᵢₘₕHₕ = Σᵢ (tᵢₕ / Tₕ) (Eₕ − Eᵢₕ) / Eₕ

F contains adjusted demographic frequencies from inferred home tracts. W contains pairwise weights from Gaussian kernels with σ = 1 km in space and σ = 1 hour in time. Spatial distance includes altitude; Ω weights observations by proximity to the hour being estimated.

Eᵢ is local racial diversity; E is diversity across the pooled weighted frequencies. tᵢ / T is the local environment’s share of that total. I report Theil’s multigroup entropy index H × 100 and use the same spatial kernel for the residential comparison.

Theory and expectations

Turn theoretical arguments into temporal expectations.

I derived hourly and weekday–weekend expectations from three theoretical perspectives on racial segregation dynamics:

  • Social isolation: racial segregation persists across daily activities.
  • Compelled mobility: segregation declines when people travel beyond their neighborhoods for work and other resources.
  • Cosmopolitanism: everyday urban life brings people into more diverse surroundings, including outside working hours.

Findings

The clearest declines coincide with the workday.

I used fixed-effects models to compare segregation across hours and days within commuting zones.

Segregation was highest overnight, declined during weekday working hours, and was generally higher on weekends. This pattern is most consistent with compelled mobility.

Friday and Saturday nights, and the following early mornings, were less segregated than Wednesday at the same hours, offering partial support for cosmopolitanism. Higher weekend segregation offered weaker support for social isolation.

Paper and code

Read the paper or explore the calculation.

Daily Dynamics of Urban Racial Segregation in the United States is available on SocArXiv.

The public replication package includes a runnable demonstration using simulated data.